The Imps, who have only lost once in their last 17 games, controlled things from the start and should have won by a much greater margin.
Simon Yeo was sent clear by Luke Foster after only two minutes but his shot was superbly blocked by Kelvin Wilson.
Then Yeo broke through again, but this time his effort brought a tremendous save from County keeper Kevin Pilkington.
Lincoln had another great chance in the 25th minute when Francis Green drew Pilkington off his line but then shot wide.
But Yeo and Green again went close before Green saw a 44th minute shot cleared off the line by Brian O'Callaghan.
City finally went in front in first half stoppage time when a long throw from Colin Cryan was hooked in by Green whose effort entered the net off the far post
Green was clear again six minutes into the second half but, after his first effort was blocked, he sent his follow up straight at Pilkington.
But County hit back and an excellent ball from Lewis McMahon found Steve Scoffham, but the striker's first time shot was beaten away by Alan Marriott.
County had a scare in the 54th minute when Pilkington slipped whilst stranded outside of his six-yard box but Green's cross was handled by Rob Ullathorne earning the County man a yellow card.
Chris Palmer missed an easy chance before making amends in the 71st minute when his free-kick was headed in by Mike Edwards for the equaliser.
Lincoln's response was to step up the pressure and within a minute Yeo shot narrowly wide with a first time effort.
Lincoln's winner came in the 80th minute when Jeff Hughes beat two defenders down the left and crossed for Jamie McCombe to head home.
Lincoln could have scored more with Green setting up Yeo but the strike somehow headed wide from inside the six-yard box. Then Lee Frecklington had a great chance but blasted over.